Polynomials & Polynomial Operations Lesson

Math Response

$$x^5\cdot x^2$$

Type answer here

Correct Answer: x^7

Deg^°

Rad

Multiple Choice

$$\left(-4x\right)^4$$

• $$256x^4$$

• $$64x^2$$

• $$-256x^4$$

• $$16x^8$$

Math Response

$$\frac{x^{10}}{x^4}$$

Type answer here

Correct Answer: x^6

Deg^°

Rad

Multiple Choice

Which of the following best describes the difference between a monomial, binomial, trinomial, and polynomial?

• A monomial has one term, a binomial has two terms, a trinomial has three terms, and a polynomial has more than three terms.

• A monomial has two terms, a binomial has three terms, a trinomial has four terms, and a polynomial has one term.

• A monomial has one variable, a binomial has two variables, a trinomial has three variables, and a polynomial has more than three variables.

• A monomial has only positive exponents, a binomial has negative exponents, a trinomial has zero exponents, and a polynomial has all types of exponents.

Categorize

Options (20)

$$2x$$  

$$-7$$  

$$x^4$$  

$$2x-9$$  

$$3x^2+8x$$  

$$5y^3$$  

$$-4z^2$$  

$$x^2 - 4$$  

$$5y + 3$$  

$$-2z + 7z^2$$  

$$x^2 + 3x + 2$$  

$$4y^2 - 5y + 1$$  

$$-2z^2 + z - 3$$  

$$5a^2 + 2a + 7$$  

$$3b^2 - 4b + 6$$  

$$x^3 + 2x^2 - 5x + 1$$  

$$4y^4 - 3y^2 + 2y + 7$$  

$$-x^5 + 6x^3 - 2$$  

$$3z^2 + z - 8$$  

$$7a^4 + 2a^3 - a + 9$$  

Classify each expression by their number of terms

Monomimal

Binomial

Trinomial

Polynomial

Video from Google Slides

Multiple Select

Which of the following expressions is a polynomial?

• $$3x^2y^4z^3$$

• 2x + 3y

• $$x^5·x^2$$

• $$4m^3-2m^2+m-2$$

Multiple Choice

Which of the following statements about the degree of a constant is correct?

• A nonzero constant has degree 0.

• A nonzero constant has degree 1.

• A nonzero constant has no degree.

• A nonzero constant has degree equal to its coefficient.

Fill in the Blanks

The degree of the monomial $16x^3y^4z^5$ is

Reorder

Reorder the following monomials or polynomials from highest degree to smallest degree

• $$7x^6y$$

• $$2abcde$$

• $$7x^3+7x^2-1$$

• $$2x^2$$

• $$21$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Fill in the Blanks

A polynomial written in standard form has its terms arranged from ___ degree to ___ degree.

Open Ended

Why is 2√xy not considered a monomial?

Multiple Select

What are the restrictions on the exponents and variables in a polynomial?

• Polynomials cannot have division by a variable

• Polynomials cannoy have fractional exponents.

• Polynomials cannot have negative exponents.

• Polynomials cannot have variables under a radical.

Multiple Choice

What is the degree of the polynomial $$10x^4-3x^3+6x^2-5x$$ ?

• 1

• 2

• 3

• 4

Multiple Choice

What is the coefficient of $$x^3$$ in the expression $$10x^4-3x^3+6x^2-5x$$ ?

• 3

• -3

• 6

• -5

Multiple Choice

Which of the following expressions represents a polynomial of degree 3?

• $$4x^3-5x^2+6x$$

• $$3x^2+6xy-9y^2$$

• $$10x^4-3x^3+6x^2-5x$$

• $$3\sqrt{x}$$

Drag and Drop

$$5abcde$$ is a ​

Placeholder

of degree ​

Placeholder

Drag these tiles and drop them in the correct blank above

monomial

5

polynomial

trinomial

binomial

2

3

1

4

0

Drag and Drop

$$3x^4+4x^2+1$$ is a ​

Placeholder

of degree ​

Placeholder

Drag these tiles and drop them in the correct blank above

monomial

5

polynomial

trinomial

binomial

2

3

1

4

0

Drag and Drop

$$\frac{2x}{3}+\frac{4}{3}$$ is a ​

Placeholder

of degree ​

Placeholder

Drag these tiles and drop them in the correct blank above

monomial

5

polynomial

trinomial

binomial

2

3

1

4

0

Multiple Choice

When adding or subtracting polynomials, what is the first step you should take?

• Combine like terms

• Multiply the coefficients

• Divide the terms

• Factor the polynomials

Multiple Select

Which of the following expressions are like terms?

• 6x^2 and 2x^2

• 3x and 9x

• -5 and -8

• 6x^2 and 9x

Math Response

$$\left(6x^2+3x-5\right)+\left(2x^2-9x-8\right)$$

Type answer here

Correct Answer: 8x^2-6x-13

Deg^°

Rad

Math Response

$$\left(8x^3+6x^2+9x\right)-\left(5x^2+4x-5\right)$$

Type answer here

Correct Answer: 8x^3+x^2+5x+5

Deg^°

Rad

Multiple Choice

$$\left(2x+8\right)\left(4x-8\right)$$

• $$8x-64$$

• $$8x^2-64$$

• $$8x^2+16x-64$$

• $$6x^2+16x-64$$

Math Response

$$\left(6x^2+6x+1\right)\left(5x^2+6x-7\right)$$

Type answer here

Correct Answer: 30x^4+66x^3-x^2-36x-7

Deg^°

Rad

Multiple Select

Which of the following expressions is a polynomial?

• $$3x^2y^4z^3$$

• 2x + 3y

• $$x^5·x^2$$

• $$4m^3-2m^2+m-2$$

Multiple Choice

Which of the following statements about the degree of a constant is correct?

• A nonzero constant has degree 0.

• A nonzero constant has degree 1.

• A nonzero constant has no degree.

• A nonzero constant has degree equal to its coefficient.

Fill in the Blanks

The degree of the monomial $16x^3y^4z^5$ is

Reorder

Reorder the following monomials or polynomials from highest degree to smallest degree

• $$7x^6y$$

• $$2abcde$$

• $$7x^3+7x^2-1$$

• $$2x^2$$

• $$21$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Fill in the Blanks

A polynomial written in standard form has its terms arranged from ___ degree to ___ degree.

Open Ended

Why is 2√xy not considered a monomial?

Multiple Select

What are the restrictions on the exponents and variables in a polynomial?

• Polynomials cannot have division by a variable

• Polynomials cannoy have fractional exponents.

• Polynomials cannot have negative exponents.

• Polynomials cannot have variables under a radical.

Multiple Choice

What is the degree of the polynomial $$10x^4-3x^3+6x^2-5x$$ ?

• 1

• 2

• 3

• 4

Multiple Choice

What is the coefficient of $$x^3$$ in the expression $$10x^4-3x^3+6x^2-5x$$ ?

• 3

• -3

• 6

• -5

Multiple Choice

Which of the following expressions represents a polynomial of degree 3?

• $$4x^3-5x^2+6x$$

• $$3x^2+6xy-9y^2$$

• $$10x^4-3x^3+6x^2-5x$$

• $$3\sqrt{x}$$

Drag and Drop

$$5abcde$$ is a ​

Placeholder

of degree ​

Placeholder

Drag these tiles and drop them in the correct blank above

monomial

5

polynomial

trinomial

binomial

2

3

1

4

0

Drag and Drop

$$3x^4+4x^2+1$$ is a ​

Placeholder

of degree ​

Placeholder

Drag these tiles and drop them in the correct blank above

monomial

5

polynomial

trinomial

binomial

2

3

1

4

0

Drag and Drop

$$\frac{2x}{3}+\frac{4}{3}$$ is a ​

Placeholder

of degree ​

Placeholder

Drag these tiles and drop them in the correct blank above

monomial

5

polynomial

trinomial

binomial

2

3

1

4

0

Multiple Choice

When adding or subtracting polynomials, what is the first step you should take?

• Combine like terms

• Multiply the coefficients

• Divide the terms

• Factor the polynomials

Multiple Select

Which of the following expressions are like terms?

• 6x^2 and 2x^2

• 3x and 9x

• -5 and -8

• 6x^2 and 9x

Math Response

$$\left(6x^2+3x-5\right)+\left(2x^2-9x-8\right)$$

Type answer here

Correct Answer: 8x^2-6x-13

Deg^°

Rad

Math Response

$$\left(8x^3+6x^2+9x\right)-\left(5x^2+4x-5\right)$$

Type answer here

Correct Answer: 8x^3+x^2+5x+5

Deg^°

Rad

Multiple Choice

$$\left(2x+8\right)\left(4x-8\right)$$

• $$8x-64$$

• $$8x^2-64$$

• $$8x^2+16x-64$$

• $$6x^2+16x-64$$

Math Response

$$\left(6x^2+6x+1\right)\left(5x^2+6x-7\right)$$

Type answer here

Correct Answer: 30x^4+66x^3-x^2-36x-7

Deg^°

Rad